Expectation Error Bounds for Transfer Learning in Linear Regression and Linear Neural Networks

In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this issue in two canonical linear settings: ordinary least squares regression and under-parameterized linear neural networks. For linear regression, we derive exact closed-form expressions for the expected generalization error with bias-variance decomposition, yielding necessary and sufficient conditions for auxiliary tasks to improve generalization on the main task. We also derive globally optimal task weights as outputs of solvable optimization programs, with consistency guarantees for empirical estimates. For linear neural networks with shared representations of width $q \leq K$, where $K$ is the number of auxiliary tasks, we derive a non-asymptotic expectation bound on the generalization error, yielding the first non-vacuous sufficient condition for beneficial auxiliary learning in this setting, as well as principled directions for task weight curation. We achieve this by proving a new column-wise low-rank perturbation bound for random matrices, which improves upon existing bounds by preserving fine-grained column structures. Our results are verified on synthetic data simulated with controlled parameters.

Fast-dVLA: Accelerating Discrete Diffusion VLA to Real-Time Performance

This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods with auxiliary training objectives can improve performance and reduce the number of convergence steps. However, they typically incur significant computational overhead due to the additional losses from auxiliary tasks. To simultaneously achieve the enhanced capabilities of auxiliary training with the simplicity of standard SFT, we decouple the two objectives of auxiliary task training within the parameter space, namely, enhancing general capabilities and fitting task-specific action distributions. To deliver this goal, we only need to train the model to converge on a small-scale task set using two distinct training strategies. The difference between the resulting model parameters can then be interpreted as capability vectors provided by auxiliary tasks. These vectors are then merged with pretrained parameters to form a capability-enhanced meta model. Moreover, when standard SFT is augmented with a lightweight orthogonal regularization loss, the merged model attains performance comparable to auxiliary finetuned baselines with reduced computational overhead. Experimental results demonstrate that this approach is highly effective across diverse robot tasks. Project page: https://chris1220313648.github.io/Fast-dVLA/

MMaDA-VLA: Large Diffusion Vision-Language-Action Model with Unified Multi-Modal Instruction and Generation

Vision-Language-Action (VLA) models aim to control robots for manipulation from visual observations and natural-language instructions. However, existing hierarchical and autoregressive paradigms often introduce architectural overhead, suffer from temporal inconsistency and long-horizon error accumulation, and lack a mechanism to capture environment dynamics without extra modules. To this end, we present MMaDA-VLA, a fully native pre-trained large diffusion VLA model that unifies multi-modal understanding and generation in a single framework. Our key idea is a native discrete diffusion formulation that embeds language, images, and continuous robot controls into one discrete token space and trains a single backbone with masked token denoising to jointly generate a future goal observation and an action chunk in parallel. Iterative denoising enables global, order-free refinement, improving long-horizon consistency while grounding actions in predicted future visual outcomes without auxiliary world models. Experiments across simulation benchmarks and real-world tasks show state-of-the-art performance, achieving 98.0% average success on LIBERO and 4.78 average length on CALVIN.

Can VLMs Reason Robustly? A Neuro-Symbolic Investigation

Vision-Language Models (VLMs) have been applied to a wide range of reasoning tasks, yet it remains unclear whether they can reason robustly under distribution shifts. In this paper, we study covariate shifts in which the perceptual input distribution changes while the underlying prediction rules do not. To investigate this question, we consider visual deductive reasoning tasks, where a model is required to answer a query given an image and logical rules defined over the object concepts in the image. Empirically, we find that VLMs fine-tuned through gradient-based end-to-end training can achieve high in-distribution accuracy but fail to generalize under such shifts, suggesting that fine-tuning does not reliably induce the underlying reasoning function. This motivates a neuro-symbolic perspective that decouples perception from reasoning. However, we further observe that recent neuro-symbolic approaches that rely on black-box components for reasoning can still exhibit inconsistent robustness across tasks. To address this issue, we propose VLC, a neuro-symbolic method that combines VLM-based concept recognition with circuit-based symbolic reasoning. In particular, task rules are compiled into a symbolic program, specifically a circuit, which executes the rules exactly over the object concepts recognized by the VLM. Experiments on three visual deductive reasoning tasks with distinct rule sets show that VLC consistently achieves strong performance under covariate shifts, highlighting its ability to support robust reasoning.

VAMPO: Policy Optimization for Improving Visual Dynamics in Video Action Models

Video action models are an appealing foundation for Vision--Language--Action systems because they can learn visual dynamics from large-scale video data and transfer this knowledge to downstream robot control. Yet current diffusion-based video predictors are trained with likelihood-surrogate objectives, which encourage globally plausible predictions without explicitly optimizing the precision-critical visual dynamics needed for manipulation. This objective mismatch often leads to subtle errors in object pose, spatial relations, and contact timing that can be amplified by downstream policies. We propose VAMPO, a post-training framework that directly improves visual dynamics in video action models through policy optimization. Our key idea is to formulate multi-step denoising as a sequential decision process and optimize the denoising policy with rewards defined over expert visual dynamics in latent space. To make this optimization practical, we introduce an Euler Hybrid sampler that injects stochasticity only at the first denoising step, enabling tractable low-variance policy-gradient estimation while preserving the coherence of the remaining denoising trajectory. We further combine this design with GRPO and a verifiable non-adversarial reward. Across diverse simulated and real-world manipulation tasks, VAMPO improves task-relevant visual dynamics, leading to better downstream action generation and stronger generalization. The homepage is https://vampo-robot.github.io/VAMPO/.

Act While Thinking: Accelerating LLM Agents via Pattern-Aware Speculative Tool Execution

LLM-powered agents are emerging as a dominant paradigm for autonomous task solving. Unlike standard inference workloads, agents operate in a strictly serial "LLM-tool" loop, where the LLM must wait for external tool execution at every step. This execution model introduces severe latency bottlenecks. To address this problem, we propose PASTE, a Pattern-Aware Speculative Tool Execution method designed to hide tool latency through speculation. PASTE is based on the insight that although agent requests are semantically diverse, they exhibit stable application level control flows (recurring tool-call sequences) and predictable data dependencies (parameter passing between tools). By exploiting these properties, PASTE improves agent serving performance through speculative tool execution. Experimental results against state of the art baselines show that PASTE reduces average task completion time by 48.5% and improves tool execution throughput by 1.8x.

Causal Neural Probabilistic Circuits

Concept Bottleneck Models (CBMs) enhance the interpretability of end-to-end neural networks by introducing a layer of concepts and predicting the class label from the concept predictions. A key property of CBMs is that they support interventions, i.e., domain experts can correct mispredicted concept values at test time to improve the final accuracy. However, typical CBMs apply interventions by overwriting only the corrected concept while leaving other concept predictions unchanged, which ignores causal dependencies among concepts. To address this, we propose the Causal Neural Probabilistic Circuit (CNPC), which combines a neural attribute predictor with a causal probabilistic circuit compiled from a causal graph. This circuit supports exact, tractable causal inference that inherently respects causal dependencies. Under interventions, CNPC models the class distribution based on a Product of Experts (PoE) that fuses the attribute predictor's predictive distribution with the interventional marginals computed by the circuit. We theoretically characterize the compositional interventional error of CNPC w.r.t. its modules and identify conditions under which CNPC closely matches the ground-truth interventional class distribution. Experiments on five benchmark datasets in both in-distribution and out-of-distribution settings show that, compared with five baseline models, CNPC achieves higher task accuracy across different numbers of intervened attributes.

Rethinking the Practicality of Vision-language-action Model: A Comprehensive Benchmark and An Improved Baseline

Vision-Language-Action (VLA) models have emerged as a generalist robotic agent. However, existing VLAs are hindered by excessive parameter scales, prohibitive pre-training requirements, and limited applicability to diverse embodiments. To improve the practicality of VLAs, we propose a comprehensive benchmark and an improved baseline. First, we propose CEBench, a new benchmark spanning diverse embodiments in both simulation and the real world with consideration of domain randomization. We collect 14.4k simulated trajectories and 1.6k real-world expert-curated trajectories to support training on CEBench. Second, using CEBench as our testbed, we study three critical aspects of VLAs' practicality and offer several key findings. Informed by these findings, we introduce LLaVA-VLA, a lightweight yet powerful VLA designed for practical deployment on consumer-grade GPUs. Architecturally, it integrates a compact VLM backbone with multi-view perception, proprioceptive tokenization, and action chunking. To eliminate reliance on costly pre-training, LLaVA-VLA adopts a two-stage training paradigm including post-training and fine-tuning. Furthermore, LLaVA-VLA extends the action space to unify navigation and manipulation. Experiments across embodiments demonstrate the capabilities of generalization and versatility of LLaVA-VLA , while real-world mobile manipulation experiments establish it as the first end-to-end VLA model for mobile manipulation. We will open-source all datasets, codes, and checkpoints upon acceptance to foster reproducibility and future research.

FRAPPE: Infusing World Modeling into Generalist Policies via Multiple Future Representation Alignment

Enabling VLA models to predict environmental dynamics, known as world modeling, has been recognized as essential for improving robotic reasoning and generalization. However, current approaches face two main issues: 1. The training objective forces models to over-emphasize pixel-level reconstruction, which constrains semantic learning and generalization 2. Reliance on predicted future observations during inference often leads to error accumulation. To address these challenges, we introduce Future Representation Alignment via Parallel Progressive Expansion (FRAPPE). Our method adopts a two-stage fine-tuning strategy: In the mid-training phase, the model learns to predict the latent representations of future observations; In the post-training phase, we expand the computational workload in parallel and align the representation simultaneously with multiple different visual foundation models. By significantly improving fine-tuning efficiency and reducing dependence on action-annotated data, FRAPPE provides a scalable and data-efficient pathway to enhance world-awareness in generalist robotic policies. Experiments on the RoboTwin benchmark and real-world tasks demonstrate that FRAPPE outperforms state-of-the-art approaches and shows strong generalization in long-horizon and unseen scenarios.

A Unified Theory of Random Projection for Influence Functions

Influence functions and related data attribution scores take the form of $g^{\top}F^{-1}g^{\prime}$, where $F\succeq 0$ is a curvature operator. In modern overparametrized models, forming or inverting $F\in\mathbb{R}^{d\times d}$ is prohibitive, motivating scalable influence computation via random projection with a sketch $P \in \mathbb{R}^{m\times d}$. This practice is commonly justified via the Johnson--Lindenstrauss (JL) lemma, which ensures approximate preservation of Euclidean geometry for a fixed dataset. However, JL does not address how sketching behaves under inversion. Furthermore, there is no existing theory that explains how sketching interacts with other widely-used techniques, such as ridge regularization and structured curvature approximations. We develop a unified theory characterizing when projection provably preserves influence functions. When $g,g^{\prime}\in\text{range}(F)$, we show that: 1) Unregularized projection: exact preservation holds iff $P$ is injective on $\text{range}(F)$, which necessitates $m\geq \text{rank}(F)$; 2) Regularized projection: ridge regularization fundamentally alters the sketching barrier, with approximation guarantees governed by the effective dimension of $F$ at the regularization scale; 3) Factorized influence: for Kronecker-factored curvatures $F=A\otimes E$, the guarantees continue to hold for decoupled sketches $P=P_A\otimes P_E$, even though such sketches exhibit row correlations that violate i.i.d. assumptions. Beyond this range-restricted setting, we analyze out-of-range test gradients and quantify a leakage term that arises when test gradients have components in $\ker(F)$. This yields guarantees for influence queries on general test points. Overall, this work develops a novel theory that characterizes when projection provably preserves influence and provides principled guidance for choosing the sketch size in practice.